Questions: Solve: 6(9y-1)-10(5y)-3y=22-4(2y-12)+8(y-6).

Transcript text: Solve: $6(9 y-1)-10(5 y)-3 y=22-4(2 y-12)+8(y-6)$. Provide your answer below: \[ y=\square \]

Solution

Solution Steps

Step 1: Expand the Equation

Start with the original equation: \[ 6(9y-1) - 10(5y) - 3y = 22 - 4(2y-12) + 8(y-6) \] Expand both sides: \[ 54y - 6 - 50y - 3y = 22 - 8y + 48 + 8y - 48 \]

Step 2: Combine Like Terms

Combine the terms on both sides: \[ (54y - 50y - 3y) = (22 + 48 - 6) \] This simplifies to: \[ y - 6 = 22 \]

Step 3: Isolate the Variable

To isolate $y$, add 6 to both sides: \[ y = 22 + 6 \] Thus, we find: \[ y = 28 \]

Final Answer

$\boxed{y = 28}$

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